Keep losing "sub" pose library after re-openning the file
See the zero next to the name of the new pose library in the first screenshot? That means it has no objects using it and so blender will thing this is unnecessary data and clean it up when the file is saved.

You can fix this by adding a 'fake user' to each pose library you want to keep using the button with a big F on it next to the pose library name when you have it selected.

This is very counter intuitive behavior.